A PRIORI ERROR ANALYSIS OF STOCHASTIC GALERKIN PROJECTION SCHEMES FOR RANDOMLY PARAMETRIZED ORDINARY DIFFERENTIAL EQUATIONS

作者：Audouze Christophe; Nair Prasanth B^*

来源：International Journal for Uncertainty Quantification, 2016, 6(4): 287-312.

DOI：10.1615/Int.J.UncertaintyQuantification.2016015843

• randomly parametrized ordinary differential equations
• generalized polynomial chaos expansions
• stochastic Galerkin projection schemes
• a priori error estimates
• temporal discretization error
• stochastic structural dynamics

Generalized polynomial chaos (gPC) based stochastic Galerkin methods are widely used to solve randomly parametrized ordinary differential equations (RODEs). These RODEs are parametrized in terms of a finite number of independent and identically distributed second-order random variables. In this paper, we derive a priori error estimates for stochastic Galerkin approximations of RODEs accounting for the temporal and stochastic discretization errors. Under appropriate stochastic regularity assumptions, convergence rates are provided for first-order linear RODE systems and first-order nonlinear scalar RODEs. We also consider the case of second-order linear RODE systems that are routinely encountered in stochastic structural dynamics applications. Finally, some insights into the long-time behavior of gPC schemes are provided for a model problem drawing on the present analysis.

• 出版日期2016